1. Field of the Invention
The present invention relates to a method of alignment adapted for use, in an exposure apparatus for exposing in succession shot areas of a wafer to a reticle pattern based on the coordinates of arrangement calculated for example by statistical processing, for aligning the shot areas of the wafer in succession.
2. Related Background Art
In the manufacture of semiconductor devices, liquid crystal display devices, thin film magnetic heads and the like with a photolithographic process, there is generally employed a projection exposure apparatus for projecting the image of a pattern of a photomask or a reticle (hereinafter collectively called reticle), through a projection optical system, onto each of shot areas of a wafer coated with a photosensitive material. Among such projection exposure apparatus, there are widely employed, in recent years, exposure apparatus of so-called step-and-repeat type, in which the wafer is placed on a two-dimensionally movable stage and is stepwise moved by said stage, whereby the shot areas of the wafer are exposed in succession to the image of the reticle pattern, particularly the exposure apparatus of reduction projection type, generally called stepper.
As an example, the semiconductor device is prepared by superposing circuit patterns of plural layers on the wafer. Therefore, in the projection exposures of the circuit patterns of the second and subsequent layers, there is required precise alignment between each shot area of the wafer, bearing already formed circuit patterns, and the image of the reticle pattern, or between the wafer and the reticle. The conventional steppers or the like have generally adopted the following enhanced global alignment method (hereinafter represented as EGA method), as described, for example, in the U.S. Pat. No. 4,780,617 issued Oct. 25, 1988.
In this EGA method, the wafer bears plural shot areas (chip pattern), each containing an alignment mark, called wafer mark, and these shot areas are arranged in a regular pattern, based on the coordinates of arrangement predetermined on the wafer. However, the wafer stepping operation based on the designed coordinates of arrangement (shot arrangement) of the plural shot areas on the wafer cannot necessarily achieve desired precise alignment of the wafer, because of the following factors:
(1) remnant rotational error .theta. of the wafer; PA1 (2) error w in orthogonality in the stage coordinate system (or in the shot arrangement); PA1 (3) linear elongation/contraction Rx, Ry of the wafer; and PA1 (4) offset (parallel displacement) Ox, Oy of the center position of the wafer.
Transformation of the wafer coordinates, corresponding to these four errors (or six parameters) can be defined by first-order equations. Consequently there can be defined the following first-order transformation model with six transformation parameters a-f, in order to transform the coordinate values of a sample coordinate system (x, y) on the wafer into those of a fixed coordinate system (X, Y) on the stage, with respect to the wafer bearing a regular arrangement of plural shot areas with wafer marks: ##EQU1##
The six parameters a-f in this transforming equation can be determined for example by minimum square approximation. In this case, a certain number of shot areas (hereinafter called sample shots) are selected from the plural shot areas (chip pattern) on the wafer, then the alignment to a reference position is conducted on each of the wafer marks, respectively associated with thus selected sample shot areas and having design coordinates (x1, y1), (x2, y2) , . . . , (xn, yn) on the coordinate system (x, y), and there are measured the coordinate values (xM1, yM1), (xM2, yM2), . . . , (xMn, yMn) on the stage coordinate system (X, Y).
The difference (.DELTA.x, .DELTA.y) between the calculated arrangement coordinate (Xi, Yi) obtained by substituting the design arrangement coordinate (xi, yi) (i=1, 2, . . . , n) of thus selected wafer marks in the above-mentioned first-order transformation model, and the measured coordinate (xMi, yMi) at the alignment is considered as the alignment error. The alignment error .DELTA.x can be represented by a summation of (Xi-xMi).sup.2 for different values of i, while the alignment error .DELTA.y can be represented by a summation of (Yi-yMi).sup.2 for different values of i.
The six transformation parameters a-f can be determined by partially differentiating these alignment errors .DELTA.x and .DELTA.y in succession with the parameters a-f and solving six simultaneous equations obtained by assuming the results of these differentiations as equal to zero. Thus the alignment of each shot area on the wafer can be achieved with the arrangement coordinates, calculated with the first-order transformation equations employing thus determined transformation parameters a-f. If the accuracy of approximation is not sufficient with such first-order transformation equations, the wafer alignment may be conducted with second- or higher-order equations.
However, the above-explained conventional technology has been associated with a drawback that, if the wafer to be exposed contains non-linear distortion, the remnant error corresponding to such non-linear distortion generates an alignment error. For this reason, the present applicant has proposed, for use in the presence of such distortion, a weighted EGA method based on a principle that the influence of non-linear error resulting from distortion becomes smaller as the distance of the shot area to be exposed (hereinafter called "exposed shot") from a predetermined reference point in the wafer to be exposed is smaller (The 40th Applied Physics Related United Symposium, Spring 1993, 31a-L-8).
In this weighted EGA method, the weighting method is linearly approximated by giving a larger weighting to a sample shot closer to the exposed shot or to the reference point (for example center of distortion) within the exposed wafer. Then the components of the correction for the offset, rotation scaling and orthogonality of wafer are determined for each exposed shot, and the exposure is conducted by setting each exposed shot at a position corrected by the above-mentioned correcting components. However, though this weighted EGA method assumes simply that the influence of distortion is smaller for the sample shot closer to the exposed shot or to the predetermined reference point, the amount of distortion may in practice be independent from the distance between the shots or to the reference point. For example, if the wafer involves a local distortion, the amount of the distortion may become large independently from the distance between the shots or the distance to the reference point. For this reason, there are encountered cases in which the alignment error resulting from the non-linear distortion cannot be reduced even with the above-explained weighted EGA method.